Okay, here are the steps to solve this problem:
a) To neutralize 15ml of 0.10 mol/L sodium carbonate solution, the hydrochloric acid solution must contain 0.015 moles of HCl.
Since the HCl solution is made by dissolving HCl gas in 100ml water, we can calculate the moles of HCl gas dissolved in 100ml:
0.015 moles HCl / 15ml sodium carbonate solution = X moles HCl gas / 100ml HCl solution
X = 0.015 * (100/15) = 0.01 moles HCl gas
b) Molar volume of HCl gas at STP is 24.45 L/mol.
So the volume of 0.01 moles HCl gas is: 0.01 moles * 24.45 L/mol = 0.2445 L
Since the solution is made with this gas in 100ml water, the volume of HCl gas dissolved in 100ml water is 0.2445 L.
So the final answers are:
a) 0.01 moles of HCl gas
b) 0.2445 L of HCl gas
Please let me know if you have any other questions!